Tire contact using two-dimensional finite elements

The problem of static contact between a tire and a nondeformable surface is explored with two-dimensional shell finite elements. The tire is treated as a composite shell, due to its nylon-corded rubber ply (laminated) construction. In the actual tire, the ply orientation angles, numbers of plies, ply thicknesses, and even the ply moduli change in the meridional direction (the direction perpendicular to the "rolling" direction). Moreover, the moduli of the materials used in construction span several orders of magnitude (isotropic rubber tread, nylon-corded rubber plies, and steel bead wires). These features present a formidable challenge to analyzing the tire with two-dimensional finite element codes. In the current work, quasi-three-dimensional behavior of the tire in static contact with a flat surface is generated through the finite element technique. The two-dimensional finite elements include the effects of transverse shear warping and thickness stretching, and use the Jaumann (local engineering) stress measures. A local and layer-wise displacement field is used to describe the behavior of the shell away from the reference surface. In contrast to stress-resultant models, this technique allows estimation of stresses and strains in individual plies, including interlaminar shea and peeling stresses.